
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) = sin(ωx + φ), where 0 < ω ≤ 12 and ω ∈ N*, and 0 < φ < π. The graph of the function is symmetric about the y-axis and is not monotonic in the interval [ \frac {π}{4}, \frac {π}{2}]. Determine the possible values of ω.

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