
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
Carl discovers a cave with three types of rocks: $6$-pound rocks worth $$16$ each, $3$-pound rocks worth $$9$ each, and $2$-pound rocks worth $$3$ each. There are at least $15$ of each type. He can carry a maximum of $20$ pounds and no more than $5$ rocks in total. What is the maximum value, in dollars, of the rocks he can carry?
**A**) $45$
**B**) $46$
**C**) $52$
**D**) $39$

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