
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and the area $S= \dfrac{1}{4}\left(a^{2}+b^{2}-c^{2}\right)$

$(1)$ Find angle $C$;  
$(2)$ If $b=2,c= \sqrt{6}$, find the value of $\cos B$.

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