
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
Kelvin the Frog was bored in math class one day, so he wrote all ordered triples \((a, b, c)\) of positive integers such that \(a \cdot b \cdot c = 2310\) on a sheet of paper. Find the sum of all the integers he wrote down. In other words, compute
$$
\sum_{\substack{a \cdot b \cdot c = 2310 \\ a, b, c \in \mathbb{N}}}(a+b+c),
$$
where \(\mathbb{N}\) denotes the positive integers.

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