
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
A random number generator issues a number \( a \), one of the natural numbers \( 1, 2, \ldots, 100 \) (with equal probability). For this value \( a \), find the maximum possible value \( M \) of the function

\[ 
f(x) = \frac{700}{x^{2} - 2x + 2a} 
\]

The probability that \( M > 10 \) is \( n \) percent. What is \( n \)?

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