
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 following equations and verify the correctness of the obtained roots:
a) \(\frac{3}{1-6x} = \frac{2}{6x+1} - \frac{8+9x}{36x^2-1}\),

b) \(\frac{3}{1-z^2} = \frac{2}{(1+z)^2} - \frac{5}{(1-z)^2}\).

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