
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
Given \(\lg 2 = 0.30103\), calculate the number of digits in \( M = 1 + 10^4 + \frac{10^4 (10^4 - 1)}{1 \cdot 2} + \frac{10^4 (10^4-1)(10^4-2)}{1 \cdot 2 \cdot 3} + \cdots + \frac{10^4 (10^4 - 1)}{1 \cdot 2} + 10^4 + 1\).

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