
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
Eighty bricks, each measuring \(3'' \times 8'' \times 15''\), are to be stacked to form a column. Each brick can be oriented to contribute \(3''\), \(8''\), or \(15''\) to the total column height. Determine how many different total column heights can be achieved using all eighty bricks.

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