
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
Find all the triples of integers  $ (a, b,c)$  such that:
\[ \begin{array}{ccc}a\plus{}b\plus{}c &\equal{}& 24 a^{2}\plus{}b^{2}\plus{}c^{2}&\equal{}& 210 abc &\equal{}& 440\end{array}\]

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