
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 the sequence $\{a_n\}$ satisfying $(a_{n+1} + a_n = (n+1) \cdot \cos \frac{n\pi}{2}$ $(n \geqslant 2, n \in \mathbb{N}^*)$, and $S_n$ is the sum of the first $n$ terms of the sequence. If $S_{2017} + m = 1010$ and $a_1 \cdot m > 0$, find the minimum value of $\frac{1}{a_1} + \frac{1}{m}$.

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