
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-five bricks, each measuring $3''\times8''\times17'',$ are to be stacked one on top of another to form a tower 85 bricks tall. Each brick can be oriented so it contributes $3''\,$, $8''\,$, or $17''\,$ to the total height of the tower. How many different tower heights can be achieved using all eighty-five of the bricks?

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