
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 internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and $A=2C$.

(Ⅰ) If $\triangle ABC$ is an acute triangle, find the range of $\frac{a}{c}$.

(Ⅱ) If $b=1, c=3$, find the area of $\triangle ABC$.

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