
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 $f(x) = (1+x)^{m} + (1+x)^{n}$ $(m \in \mathbb{N}^*, n \in \mathbb{N}^*)$, the coefficient of the $x$ term in the expansion of $f(x)$ is $15$. Find the minimum value of the coefficient of the $x^{2}$ term.

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