
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
Let \( f(m, n) = 3m + n + (m + n)^2 \). Find \( \sum_{m=0}^{\infty} \sum_{n=0}^{\infty} 2^{-f(m, n)} \).

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