
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
1. \( x^2 + 10x = 56 \)
2. \( 4x^2 + 48 = 32x \)
3. \( x^2 + 20 = 12x \)
4. \( 3x^2 - 36 = 32x - x^2 \)
5. \( x^2 + 8x = 20 \)
6. \( 3x^2 = 12x + 63 \)
7. \( x^2 + 16 = 8x \)
8. \( 6x^2 + 12x = 90 \)
9. \( \frac{1}{2} x^2 + x = 7 \frac{1}{2} \)

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