
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
Let \[M=\frac{\sqrt{\sqrt{8}+3}+\sqrt{\sqrt{8}-3}}{\sqrt{\sqrt{8}+2}}-\sqrt{5-2\sqrt{6}},\] calculate the value of $M$.

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