
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 $a$, $b$, and $c$, respectively. Given vectors $\overrightarrow{m} = (b, c-a)$ and $\overrightarrow{n} = (\sin C + \sin A, \sin C - \sin B)$, and $\overrightarrow{m}$ is parallel to $\overrightarrow{n}$.
(1) Find angle $A$;
(2) If $b+c=4$, and the area of $\triangle ABC$ is $\dfrac{3\sqrt{3}}{4}$, find the length of side $a$.

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