
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
117. Solve the equations:

a) \((x + a)(x + 2a)(x + 3a)(x + 4a) = 3a^4\);

b) \(x^2 + \frac{4}{x^2} + 6\left(x + \frac{2}{x}\right) = 23\);

c) \(\sqrt[5]{\frac{16x}{x-1}} + \sqrt[5]{\frac{x-1}{16x}} = \frac{5}{2}\).

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