
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and they satisfy $(\frac{5}{4}c - a)\cos B = b \cos A$.
(1) If $\sin A = \frac{2}{5}$ and $a + b = 10$, find $a$;
(2) If $b = 3\sqrt{5}$ and $a = 5$, find the area $S$ of $\triangle ABC$.

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