
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 quadratic equations:
1) \( 5x^{2} = 40x \)
2) \( \frac{25}{9} x^{2} = 100 \)
3) \( 10x = x^{2} + 21 \)
4) \( x^{2} = 12x + 288 \)
5) \( x^{2} + 20\frac{1}{4} = 11\frac{1}{4} x \)
6) \( \frac{1}{12} x^{2} + \frac{7}{12} x = 19 \)

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