
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 $n$. Let $m$ be the least positive integer such that
\[x_m\leq 6+\frac{1}{2^{18}}.\]
In which of the following intervals does $m$ lie?
A) [9, 26]
B) [27, 80]
C) [81, 242]
D) [243, 728]
E) [729, Infinity)

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