
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
Fifty bricks, each measuring $5'' \times 12'' \times 18''$, are stacked to form a tower. Each brick can be oriented to add $5''$, $12''$, or $18''$ to the total tower height. How many different tower heights can be achieved using all fifty bricks?

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