To handle this order processing system, you can use a finite state machine $($FSM$)$ or workflow

logic. Here's a simplified outline of how this process could be managed:

### States:

$1.**$Order Placed$**$: Initial state when the order is placed.

$2.**$Waiting for Cancellation$**$: The system waits for either a cancellation request or for $24$ hours

to elapse.

$3.**$Order Canceled$**$: The order is canceled if a cancellation request is received within $24$

hours.

$4.**$Order Shipped$**$: The order is processed for shipping if no cancellation request is received

within $24$ hours.

### Transitions:

$1.**$Order Placed to Waiting for Cancellation$**$: Automatically transitions when the order is

placed.

$2.**$Waiting for Cancellation to Order Canceled$**$: Transitions if a cancellation request is

received within $24$ hours.

$3.**$Waiting for Cancellation to Order Shipped$**$: Transitions if no cancellation request is

received within $24$ hours.

### Pseudocode Implementation:

$```$python

import time

from threading import Timer

class OrderProcessingSystem:

def $\_\_$init$\_\_($self$,$ order$\_$id$)$:

self.order$\_$id $=$ order$\_$id

self.state $=$ "Order Placed"

self.timer $=$ None

def place$\_$order$($self$)$:

self.state $=$ "Waiting for Cancellation"

print$($f$"$Order $\{$self$.$order$\_$id$\}$ placed. Waiting for cancellation or $24$ hours to elapse."$)$

self.timer $=$ Timer$(24*60*60,$ self.proceed$\_$to$\_$shipping$)$ # $24-$hour timer

self.timer.start$()$

def cancel$\_$order$($self$)$:

if self.state $==$ "Waiting for Cancellation":

self.state $=$ "Order Canceled"

if self.timer:

self.timer.cancel$()$

print$($f$"$Order $\{$self$.$order$\_$id$\}$ canceled. Cancellation confirmation sent to customer."$)$

else:

print$($f$"$Order $\{$self$.$order$\_$id$\}$ cannot be canceled. Current state: $\{$self$.$state$\}")$

def proceed$\_$to$\_$shipping$($self$)$:

if self.state $==$ "Waiting for Cancellation":

self.state $=$ "Order Shipped"

print$($f$"$Order $\{$self$.$order$\_$id$\}$ processed for shipping. Order sent to customer."$)$

# Usage example

order$\_$system $=$ OrderProcessingSystem$($order$\_$id$=12345)$

order$\_$system.place$\_$order$()$

# Simulate a cancellation request within $24$ hours

time.sleep$(5)$ # Simulating a delay before cancellation request

order$\_$system.cancel$\_$order$()$

$```$

### Explanation:

$1.**$Order Placed$**$: The $`$place$\_$order$`$ method transitions the state to "Waiting for Cancellation"

and starts a $24-$hour timer.

$2.**$Waiting for Cancellation$**$: The system waits in this state. If $`$cancel$\_$order$`$ is called, the

state changes to "Order Canceled", and the timer is canceled. If the $24-$hour timer elapses, the

$`$proceed$\_$to$\_$shipping$`$ method is called, transitioning the state to "Order Shipped".

$3.**$Order Canceled$**$: If a cancellation request is received within $24$ hours, the order is

canceled, and a confirmation message is sent to the customer.

$4.**$Order Shipped$**$: If no cancellation request is received within $24$ hours, the order proceeds

to shipping, and a shipping confirmation message is sent to the customer.

This implementation ensures that the order processing system correctly handles the order state

transitions based on customer actions and time constraints.