
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
In the triangular pyramid $S-A B C$, $\triangle A B C$ is an equilateral triangle with side length 4. The plane $SAC$ is perpendicular to the plane $ABC$, and $SA = SC = 2 \sqrt{3}$. Points $M$ and $N$ are the midpoints of $AB$ and $SB$, respectively.
(1) Find the measure of the dihedral angle $N-C M-B$.
(2) Find the distance from point $B$ to the plane $CMN$.

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