
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
Solve the equations:
1) \(x|x|=4\)
2) \((x-3)^{2}=1-\pi\)
3) \(\left|-1-x^{2}\right|=5\)
4) \(x^{2}-3x+x^{-1}=x^{-1}\)
5) \((\sqrt{x-2})^{4}=|x|-x\)
6) \(x(x-5)=x^{2}-5|x|\).

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