
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
A rectangular prism has a volume of 720 cubic units, where $a, b,$ and $c$ are integers and $1 < c < b < a$. Find the maximum possible value of $b$ if $c=3$, while ensuring $a$, $b$, and $c$ are distinct prime factors.

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