
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 equations by an appropriate method:
1. $x^2 - 6x + 9 = (5 - 2x)^2$
2. $5x^2 - 2x - (x^2 - 2x + 4) = 0$
3. $3x^2 - 2x + 1 = 0$
4. $9x^2 + 6x - 3 = 0$
5. $x^2 - 11x + 28 = 0$
6. $4x^2 + 4x + 10 = 1 - 8x$

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