
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
Consider a sequence defined recursively by \( x_0 = 3 \) and
\[
x_{n+1} = \frac{x_n^2 + 4x_n + 6}{x_n + 4}
\]
for all nonnegative integers \( n \). Determine the smallest positive integer \( m \) such that
\[
x_m \leq 3 + \frac{1}{2^{10}}
\].
A) 0
B) 1
C) 2
D) 10
E) 100

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