
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 function f(x) = $$\begin{cases} \cos{x}, & |\cos{x}| \geq \frac{\sqrt{2}}{2} \\ 0, & |\cos{x}| < \frac{\sqrt{2}}{2} \end{cases}$$, find f($\frac{\pi}{3}$), and the solution set for f(x) ≤ sin(x) when 0 ≤ x ≤ 2π.

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