
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 $A$, $B$, $C$ are $a$, $b$, $c$ respectively.
(1) If $2a\sin B= \sqrt {3}b$, $A$ is an acute angle, find the value of $A$;
(2) If $b=5$, $c= \sqrt {5}$, $\cos C= \frac {9}{10}$, find the value of $a$.

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