A gas contained inside a closed piston$-$cylinder device undergoes three processes.

Process $1-2$: Expansion during which $PV=$ constant $($polytropic process with $n=1)$

Process $2-3$: Constant volume

Process $3-1$: Constant pressure

$($a$)$ Is this a power cycle or a heat pump cycle? Explain.

$($b$)$ If it is a power cycle, find its thermal efficiency. If it is a heat pump cycle, find its $($heating$)$ coefficient

of performance.