
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
Given $2C_a^2 - (C_a^1 - 1)A_3^2 = 0$, and the expansion of $\left(x^{3} + \frac {b}{x^{2}}\right)^{a}$ ($b \neq 0$), the coefficient of the $x^{13}$ term is -12, find the real number $b$.

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