
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
Suppose that  $f$  is a function on the interval  $[1,3]$  such that  $-1\le f(x)\le 1$  for all  $x$  and  $\displaystyle \int_1^3f(x)\,dx=0.$  How large can  $\displaystyle\int_1^3\frac{f(x)}x\,dx$  be?

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