
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:

a) \(2 x + 1 + x^{2} - x^{3} + x^{4} - x^{5} + \ldots = \frac{13}{6}\), where \(|x| < 1\);

b) \(\frac{1}{x} + x + x^{2} + \ldots + x^{n} + \ldots = \frac{7}{2}\), where \(|x| < 1\).

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