
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 \( P = 35^5 + 5 \times 35^4 + 10 \times 35^3 + 10 \times 35^2 + 5 \times 35 + 1 \). Determine the number of positive integer factors of \( P \).

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A) 36  
B) 100  
C) 121  
D) 216  
E) 400  

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