
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
The graphs of the functions $y=\sin(\omega x + \phi)$ and $y=\cos(\omega x + \phi)$, where $\phi > 0$ and $|\phi| < \frac{\pi}{2}$, have exactly three different intersection points P, M, and N, on the interval $x\in[0, \frac{5\sqrt{2}}{2}]$. If triangle $\triangle PMN$ is a right triangle, determine the range of $\phi$.

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