
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 be $y=\sin \left( \frac {\pi}{2}x+ \frac {\pi}{3}\right)$. If for any $x\in\mathbb{R}$, there exist $x_{1}$ and $x_{2}$ such that $f(x_{1})\leqslant f(x)\leqslant f(x_{2})$ always holds, then the minimum value of $|x_{1}-x_{2}|$ is \_\_\_\_\_\_.

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