
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 rectangular box has dimensions $a \times b \times c$, where $a$, $b$, and $c$ are integers under the constraints $1\leq a \leq b \leq c$. Determine the number of ordered triples $(a, b, c)$ for which the volume is $abc$ and the surface area is $3(ab + bc + ac)$, with $a, b, c \leq 10$.

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