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

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