
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 a function $f(x) = x^m + ax$ (where $m$ and $a$ are constants) has the derivative $f'(x) = 2x + 1$, find the sum of the first $n$ terms of the sequence $\left\{ \frac {f(n)}{n \cdot 2^n} \right\} (n \in \mathbb{N}^*)$.

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