
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 following equations:

(1) 3x² - 5x - 2 = 0

(2) x² - 1 = 2(x + 1)

(3) 4x² + 4x + 1 = 3(3 - x)²

(4) (2x + 8)(x - 2) = x² + 2x - 17

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