
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
For a positive constant  $p$ , let  $f(x)=\int_{-1}^x \{p-\ln (1+|t|)\}\ dt.$ (1) Find the extreme value of  $f(x)$ .

(2) Find the range of  $p$  such that the curve  $y=f(x)$  has two point of intersections with the positive part of the  $x$  axis.

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