
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
Natural numbers \( a, b, c \) are such that \( 1 \leqslant a < b < c \leqslant 3000 \). Find the largest possible value of the quantity

$$
\gcd(a, b) + \gcd(b, c) + \gcd(c, a)
$$

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