
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
Identical gases are in two thermally insulated vessels with volumes \( V_{1}=2 \) L and \( V_{2}=3 \) L. The pressures of the gases are \( p_{1}=3 \) atm and \( p_{2}=4 \) atm, and their temperatures are \( T_{1}=400 \) K and \( T_{2}=500 \) K respectively. The gases are mixed. Determine the temperature that will be established in the vessels.

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