
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
What digit should be placed in the position marked with a question mark (?) to make the resulting integer divisible by 7:
$$
\underbrace{666 \cdots 66}_{\text{50 digits of 6}}?\underbrace{555 \cdots 55}_{50 digits of 5}
$$
(Leningrad Mathematical Olympiad, 1989)

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