
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
Let \( f(x) \) be a function defined on \( \mathbf{R} \) such that
$$
\left| f(x) + \cos^2(x) \right| \leq \frac{3}{4}, \quad \left| f(x) - \sin^2(x) \right| \leq \frac{1}{4}.
$$

Find the explicit form of the function \( f(x) \).

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