
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
Sixty bricks, each measuring $2''\times6''\times15''$, are to be laid one on top of the other to construct a column. Each brick can be oriented so it contributes $2''$, $6''$, or $15''$ to the total height of the column. Determine how many distinct total heights can be reached using all sixty bricks.

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