
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 an ideal gas undergoes a closed cycle in which:

$1-2$ - isobaric process, where the volume increases by 4 times;

$2-3$ - isothermal process, where the pressure increases;

$3-1$ - process in which the gas is compressed according to the law $T=\gamma V^{2}$.

Determine by what factor the volume in state 3 exceeds the initial volume in state 1.

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