
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 $y=f(2x+ \frac {\pi}{6})$, then the value of $\varphi$ is \_\_\_\_\_\_.

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