
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 that the sum of the first $n$ terms of the sequence ${a_n}$ is ${S_n}=({-1})^{n+1}\frac{1}{{{2}^{n}}}$, if there exists a positive integer $n$ such that $(p-a_{n})(p-a_{n+1}) < 0$ holds true, then the range of the real number $P$ is ________.

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