
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 $V_{1}=1$ L and $V_{2}=2$ L. The gas pressures are $p_{1}=2$ atm and $p_{2}=3$ atm, and their temperatures are $T_{1}=300$ K and $T_{2}=400$ K, respectively. The gases are mixed. Determine the temperature that will be established in the vessels after mixing.

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