
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
If
\[
M = \frac{\sqrt{3 + \sqrt{8}} + \sqrt{3 - \sqrt{8}}}{\sqrt{2\sqrt{2} + 1}} - \sqrt{4 - 2\sqrt{3}},
\]
then $M$ equals...
A) $2 - \sqrt{2}$
B) $3$
C) $3 - \sqrt{3}$
D) $\sqrt{5}$
E) none of these

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