
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 a triangle $ABC$ with its internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$, respectively, where angle $A$ is acute and $\sqrt{3}b=2a\sin B$.

(1) Find the measure of angle $A$.
(2) If $a=7$ and the area of triangle $ABC$ is $10\sqrt{3}$, find the value of $b^2+c^2$.

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