
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
\[
x_{n+1}=\frac{x_n^2+7x_n+10}{x_n+8}
\]
for all nonnegative integers $n$. Let $m$ be the least positive integer such that
\[
x_m\leq 6+\frac{1}{2^{24}}.
\]
Find the interval in which $m$ lies.
A) [0, 50]
B) [51, 80]
C) [81, 242]
D) [243, 500]
E) [501, ∞)

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