
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 \[M=\frac{\sqrt{\sqrt{7}+4}+\sqrt{\sqrt{7}-4}}{\sqrt{\sqrt{7}+2}}-\sqrt{5-2\sqrt{6}},\] then determine the value of $M$.
A) $\frac{\sqrt{2}}{2}$  
B) $\frac{\sqrt{2}}{2} - 1$  
C) $\frac{\sqrt{7}}{2}$  
D) $\frac{\sqrt{7}}{2} - 1$  
E) $\frac{\sqrt{14}}{2} - 1$

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