
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
Two connected rooms have different sizes and temperatures. One room has a length of $5 \,\mathrm{m}$, a width of $3 \,\mathrm{m}$, a height of $4 \,\mathrm{m}$, and a temperature of $22 \,^{\circ}\mathrm{C}$; the other room has a length of $6 \,\mathrm{m}$, a width of $5 \,\mathrm{m}$, a height of $4 \,\mathrm{m}$, and a temperature of $13 \,^{\circ}\mathrm{C}$. What will be the common temperature after opening the door between the rooms?

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