
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
Suppose $a$, $b$, and $c$ are positive numbers satisfying:
\begin{align*}
a^2/b &= 2, \\
b^2/c &= 4, \text{ and} \\
c^2/a &= 6.
\end{align*}
Find the value of $a$.

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