
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 $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\sin A + \sin C = p \sin B (p \in \mathbb{R})$, and $ac = \frac{1}{4}b^2$.

(1) When $p = \frac{5}{4}, b = 1$, find the values of $a$ and $c$.
(2) If angle $B$ is acute, find the range of $p$.

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