
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 $f(x)=\begin{cases} 2\cos \frac{\pi }{2}x, & |x|\leqslant 1, \\ x^{2}-1, & |x| > 1 \end{cases}$, if $|f(x)+f(x+l)-2|+|f(x)-f(x+l)|\geqslant 2$ ($l > 0$) holds for any real number $x$, then the minimum value of $l$ is.

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