
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
Let \( A = 100101102103 \cdots 798799 \) be a 2100-digit positive integer formed by connecting the three-digit numbers from 100 to 799 in sequence. What is the remainder when \( A \) is divided by 126?

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