
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) $(2x - 4)(x - 5) < 0$;
(2) $3x^{2} + 5x + 1 > 0$;
(3) $-x^{2} + x < 2$;
(4) $7x^{2} + 5x + 1 \leq 0$;
(5) $4x \geq 4x^{2} + 1$.

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