
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 that 6-pound rocks are valued at $18 each, 3-pound rocks are valued at $9 each, and 2-pound rocks are valued at $6 each, and that Alice can carry at most 21 pounds and has at least 15 of each size available, determine the maximum value of the rocks Alice can carry out of the cave.

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