
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
Given that $A$, $B$, and $C$ are the three internal angles of $\triangle ABC$, and $a$, $b$, and $c$ are their corresponding sides, vector $\overrightarrow{m}=(-1, \sqrt {3})$, $\overrightarrow{n}=(\cos A,\sin A)$, and $\overrightarrow{m} \cdot \overrightarrow{n}=1$
(1) Find angle $A$;
(2) If $c= \sqrt {5}$, $\frac {\cos B}{\cos C}= \frac {b}{c}$, find the area $S$ of $\triangle ABC$.

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