
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
Aida made three cubes with positive integer side lengths  $a,b,c$ . They were too small for her, so she divided them into unit cubes and attempted to construct a cube of side  $a+b+c$ . Unfortunately, she was  $648$  blocks off. How many possibilities of the ordered triple  $\left(a,b,c\right)$  are there?

*2017 CCA Math Bonanza Team Round #9*

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