
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
Let \(a\), \(b\), and \(c\) be positive numbers satisfying:
\[
a^3/b^2 = 4, \\
b^4/c^3 = 8, \\
c^5/a^4 = 32.
\]
Find the value of \(a\).

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