
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
If $f(x) = 2\sin(\omega x + \phi) - 3$, where $\omega > 0$, and for all $x \in \mathbb{R}$, the equation $f(x + \frac{\pi}{6}) = f(\frac{\pi}{3} - x)$ holds true, then find the value of $f(\frac{\pi}{4})$.

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