
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
Define a sequence recursively by $x_0=7$ and
\[
x_{n+1} = \frac{x_n^2 + 6x_n + 5}{x_n + 7}
\]
for all nonnegative integers $n$. Determine the least positive integer $m$ such that
\[
x_m \leq 5 + \frac{1}{2^{10}}.
\]
A) 70
B) 89
C) 105
D) 150

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