
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 the function f(x)=4cos(ωx+φ) for any $x\in \mathbb{R}$, satisfy f(-x)=f(π/3+x) and the function g(x)=sin(ωx+φ)-2. Evaluate the value of g(π/6).

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