
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

For each pair of numbers $\overline{a b b}$ and $\overline{a b b}$, where $a$ and $b$ are distinct digits, the GCD of these numbers was calculated. Find the largest of these GCDs.

$\overline{a b b}$ is the standard notation for a number consisting of the digits $a, b, and b$ in that exact order.

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