
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
For which negative integer values of \( n \) is the function \( f \), defined by the equation

\[ 
f(x) = \cos 7x \cdot \sin \frac{25x}{n^2} 
\]

a periodic function with period \( T = 7\pi \)?

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