
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
Determine the largest number among those $A$ values for which the following statement holds. No matter in what order we write down the first 100 positive integers, there will always be ten consecutive numbers in the sequence whose sum is at least $A$.

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