
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

If there exists a positive number $p$ such that for all $x$, $f(x + p) = f(x)$, then $f(x)$ is a periodic function. For example, $\sin x$ is a periodic function with a period of $2\pi$. Is $\sin\left(x^2\right)$ a periodic function?

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