
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
Given rocks of three different types are available: 6-pound rocks worth $18 each, 3-pound rocks worth $9 each, and 2-pound rocks worth $3 each, and there are at least 15 rocks available for each type. Carl can carry at most 20 pounds. Determine the maximum value, in dollars, of the rocks Carl can carry out of the cave.

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