
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~ is~ the~ maximum~ number~ of~ distinct~ integers~ in~ a~ row~ such~ that~ the~sum~ of~ any~ 11~ consequent~ integers~ is~ either~ 100~ or~ 101~?$ I'm posting this problem for people to discuss

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