
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
In a container with a piston and heat-conductive walls, there is nitrogen with a volume of \( V_{0}=1 \mathrm{~m}^{3} \), pressure of \( 10^{5} \mathrm{~Pa} \), and temperature of \( 300 \mathrm{~K} \). We perform two experiments with the gas.

a) We change the state of the gas in such a way that the ratio \( \Delta p / \Delta V \) remains constant at a value \( a_{1} \). We observe that, whether we increase or decrease the volume compared to \( V_{0} \), the nitrogen always cools down.

b) In the second case, we ensure that \( \Delta p / \Delta V = a_{2} \) remains constant. Now, we observe that whether we decrease or increase the volume compared to \( V_{0} \), the system releases heat to its surroundings.

Determine the values of \( a_{1} \) and \( a_{2} \).

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