
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. $|2x-1|<15$
2. $x^2+6x-16<0$
3. $|2x+1|>13$
4. $x^2-2x>0$

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