
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 $ABC$, with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, it is given that $a=2b$ and that $\sin A$, $\sin C$, $\sin B$ form an arithmetic sequence.
(1) Find the value of $\cos A$;  
(2) If the area of triangle $ABC$ is $S_{\triangle ABC} = \frac {8 \sqrt {15}}{3}$, find the value of $c$.

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