
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 has a collection of $6$-pound rocks worth $$16$ each, $3$-pound rocks worth $$9$ each, and $2$-pound rocks worth $$3$ each, with at least $30$ of each size. Determine the maximum value, in dollars, of the rocks he can carry out of the cave, given that he can carry at most $24$ pounds and no more than $4$ rocks of any size.

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