$-------$Please provide me with a tree written in hand for Q$5------------$

A robot on Mars is trying to help an astronaut reach the base station $15$ kilometers away. The

robot has limited fuel, and it must find the most efficient way to travel to the base. The goal is to

help the astronaut reach the base while saving fuel.

The robot can do these actions:

$$ Move forward some distance, which uses fuel.

$$ Drop extra fuel at a specific location to use later.

$$ Refill fuel from a location where it has dropped fuel earlier.

Robot's rules:

$$ The robot starts with $3$ fuel capsules.

$$ Each fuel capsule lets the robot move up to $9$ kilometers.

$$ If the robot runs out of fuel, it must return to where it dropped extra fuel to refuel.

Questions

$1.$ Propose a simple state representation.

$2.$ What is the initial state?

$3.$ What is the goal state?

$4.$ What are the actions?

$5.$ Draw the state space using Uniform Cost Search $($UCS$),$ considering all possible actions

the robot can take. Create a simple tree that shows how the robot moves and where it

refuels, until it reaches the base $($stop after showing $3$ levels of the tree$).$

$6.$ What kind of environment is this problem set in$?$

$7.$ What type of agent is the robot? Explain your answers.