
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 \[ M = \frac{\sqrt{\sqrt{7}+3} + \sqrt{\sqrt{7}-3}}{\sqrt{\sqrt{7}+2}} - \sqrt{5-2\sqrt{6}}, \] then $M$ equals?
- **A)** $\frac{\sqrt{57} - 6\sqrt{6} + 4}{3}$
- **B)** $\sqrt{2} - 1$
- **C)** $\frac{1 + \sqrt{57}}{3}$
- **D)** $\sqrt{57} - 2\sqrt{6}$
- **E)** $\frac{1}{2}\sqrt{\frac{15}{2}}$

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