
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
Given $f(x) = (1+x)^m + (1+x)^n (m,n \in \mathbb{N}^*)$, find the minimum coefficient of $x^2$ in the expansion of $f(x)$, and find the sum of the coefficients of the odd powers of $x$ when $x^2$'s coefficient is at its minimum.

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