
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
Let the function $f(x)=2\sin \left( \frac{\pi}{2}x+ \frac{\pi}{5} \right)$. If for any $x\in\mathbb{R}$, $f(x_{1})\leqslant f(x)\leqslant f(x_{2})$ holds, then calculate the minimum value of $|x_{1}-x_{2}|$.

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