
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 must be put in place of the " $?$ " in the number  $888...88?999...99$  (where the  $8$  and  $9$  are each written  $50$  times) in order that the resulting number is divisible by  $7$ ? 

(M . I. Gusarov)

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