
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
Dima has 25 identical bricks of size $5 \times 14 \times 17$. Dima wants to construct a single tower using all of his bricks, each time adding one brick on top (each new brick adds 5, 14, or 17 to the current height of the tower). A number $n$ is called constructible if Dima can build a tower with a height of exactly $n$. How many constructible numbers exist?

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