
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 $\{a_n\}$ with the sum of the first $n$ terms $S_n = (-1)^n \cdot n$, if for any positive integer $n$, the inequality $(a_{n+1} - p)(a_{n} - p) < 0$ always holds, then the range of the real number $p$ is __________.

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