
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
One rainy afternoon you write the number  $1$  once, the number  $2$  twice, the number  $3$  three times, and so forth until you have written the number  $99$  ninety-nine times. What is the  $2005$  th digit that you write?

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