
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 coefficient of \(x^2\) in the expansion of \((x \cos \theta + 1)^5\) is equal to the coefficient of \(x^3\) in the expansion of \(\left(x + \frac{5}{4}\right)^4\), find \(\cos \theta\).

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