
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
Let $f(x) = \sin^2x + \sqrt{3}\sin x\cos x - \frac{1}{2} \ (x \in \mathbb{R})$.
1. Find the smallest positive period and the range of the function $f(x)$.
2. Given a triangle $ABC$ with the opposite sides of angles $A$, $B$, $C$ being $a$, $b$, $c$ respectively, and angle $A$ is acute, $a=2\sqrt{3}, c=4$. If $f(A)=1$, find $A$ and $b$.

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