
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 graph of the function $f(x)=\sin 2x$ is shifted to the right by $\varphi(0 < \varphi < \frac{\pi}{2})$ units to obtain the graph of the function $g(x)$. If for $x_{1}$, $x_{2}$ satisfying $|f(x_{1})-g(x_{2})|=2$, we have $|x_{1}-x_{2}|_{\min }=\frac{\pi}{3}$, calculate $\varphi$.

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