
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
One mole of a monatomic ideal gas undergoes a cyclic process $a b c a$. The diagram of this process in $P-T$ coordinates forms a curvilinear triangle, where side $a b$ is parallel to the $T$ axis, side $b c$ is a line segment passing through the origin, and side $ca$ is an arc of a parabola passing through the origin with its axis parallel to the $T$ axis. At points $a$ and $c$, the temperature of the gas is the same and equal to $T_{0}=320 \mathrm{~K}$. The pressure at point $a$ is half the pressure at point $c$. Determine the work done by the gas over the cycle.

Present the answer in LaTex format: \boxed{Your answer}
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