
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 \[x_{n+1}=\frac{x_n^2+6x_n+8}{x_n+7}\] for all nonnegative integers $n.$ Let $m$ be the least positive integer such that
\[x_m\leq 5+\frac{1}{2^{15}}.\]
A) 192
B) 204
C) 207
D) 213
E) 220

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