
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
21. In $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$, respectively, and $\dfrac{\cos B}{\cos C} = -\dfrac{b}{2a+c}$.

(1) Find the size of angle $B$;

(2) If $b = \sqrt{13}$, $a + c = 4$, find the area of $\triangle ABC$.

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