
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 sequence \(\left\{a_{n}\right\}\) where \(a_{n} + a_{n+1} = n \cdot (-1)^{\frac{n(n+1)}{2}}\), with the sum of the first \(n\) terms being \(S_{n}\), and \(m + S_{2015} = -1007\), and \(a_{1} \cdot m > 0\). Find the minimum value of \(\frac{1}{a_{1}} + \frac{4}{m}\).

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