
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 $f(x) = \sin x \cos \varphi + \cos x \sin \varphi$ (where $x \in \mathbb{R}$, $0 < \varphi < \pi$). If the point $\left( \frac{\pi}{6}, \frac{1}{2} \right)$ is on the graph of the function $y = f\left(2x + \frac{\pi}{6}\right)$, then the value of $\varphi$ is \_\_\_\_\_\_.

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