
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 cyclic process described by the equation

$$
\left(\frac{P}{P_{0}}-a\right)^{2}+\left(\frac{T}{T_{0}}-b\right)^{2}=c^{2}
$$

where \( P_{0}, T_{0}, a, b, c \) are constants, and \( c^{2} < a^{2} + b^{2} \). Determine the minimum volume of the gas in this process.

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