
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 $\triangle ABC$, $a$, $b$, $c$ are the lengths of the sides opposite to angles $A$, $B$, $C$ respectively, and $8ab\sin C = 3(b^{2} + c^{2} - a^{2})$. If $a = \sqrt{10}$ and $c = 5$.

(I) Find $\cos A$.

(II) Find the area $S$ of triangle $\triangle ABC$.

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