
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) = A sin(ωx + φ) (A > 0, ω > 0, |φ| < $\frac{π}{2}$), x = $-\frac{π}{4}$ is a zero point of the function, and x = $\frac{π}{4}$ is one of its symmetric axes. Determine the maximum value of ω such that ($\frac{π}{9}$, $\frac{π}{6}$) is a monotonic interval of f(x).

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