
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
If the variable $a$ is equal to $b^2$ when $c = 3$, and the sum of $b$ and $c$ is twice $a$, determine the product $a \cdot b$ when $c = 3$ and $b + c = b \cdot c$ where $a, b,$ and $c$ are positive numbers.
A) $\frac{15}{4}$
B) $\frac{27}{8}$
C) $\frac{3}{2}$
D) $\frac{9}{4}$

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