
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) \(x^{4} + 5x^{2} = 126\)

2) \(x^{4} + 24 = 10x^{2}\)

3) \(x^{4} = 2x^{2} + 8\)

4) \(x^{6} = 3x^{3} + 40\)

5) \(x^{7} = bx^{5} + cx^{3}\)

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