
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 inequalities:
1) \( |x-6| \leq 2 \)
2) \( (x+3)^{2} < 1 \)
3) \( |x| > x \)
4) \( \left|x^{2}-4x-5\right| > x^{2}-4x-5 \)

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