
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 $\triangle ABC$ with internal angles $A$, $B$, $C$ and their opposite sides $a$, $b$, $c$ respectively, it satisfies the equation $\frac{2b-c}{a} = \frac{\cos C}{\cos A}.$
- (I) Find the measure of angle $A$.
- (II) If the segments with lengths $p\sin A$, $\sin B$, $\sin C$ can form a right triangle with $p\sin A$ as the hypotenuse, determine the range of values for the real number $p$.

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