
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
Translate the graph of the function $f(x) = \sin(2x + \theta)$ ($|\theta| < \frac{\pi}{2}$) to the right by $\varphi$ ($0 < \varphi < \pi$) units to obtain the graph of the function $g(x)$. If both graphs of $f(x)$ and $g(x)$ pass through point $P(0, \frac{1}{2})$, then $\varphi = \_\_\_\_\_\_$.

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