
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 translated to the right by $\phi (0 < \phi < \frac{\pi}{2})$ units to obtain the graph of the function $g(x)$. If for $x_{1}$ and $x_{2}$ that satisfy $|f(x_{1})-g(x_{2})|=2$, we have $|x_{1}-x_{2}|_{\min}= \frac{\pi}{3}$, then find the value of $\phi$.

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