
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 that the graph of the function y = tan(x) defined on the interval (0, $\frac{\pi}{2}$) intersects with the graph of y = sin(ωx) (ω > 0) at exactly one point P, find the value of ω when the x- and y-coordinates of point P are at their maximum.

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