
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) $|5-x| > 6$;
(2) $\left|x^{2}+9 x-1\right| \leqslant 9$;
(3) $3 \leqslant |4 x-1| < 7$;
(4) $\left|\frac{x+1}{x-1}\right| \geqslant 2$.

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