
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 distance between adjacent symmetry axes in the graph of the function $f(x) = \sin(\omega x + \varphi)$ $(\omega > 0, 0 < \varphi < \pi)$ is $\frac{\pi }{2}$. Given that the terminal side of angle $\varphi$ passes through the point $(3,\sqrt{3})$, find the value of $f\left(\frac{\pi }{4}\right)$.

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