
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
A mason has bricks with dimensions  $2\times5\times8$  and other bricks with dimensions  $2\times3\times7$ . She also has a box with dimensions  $10\times11\times14$ . The bricks and the box are all rectangular parallelepipeds. The mason wants to pack bricks into the box filling its entire volume and with no bricks sticking out.
Find all possible values of the total number of bricks that she can pack.

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