
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 $ABC$, let the sides opposite to angles $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively, $\overrightarrow{AB}\cdot\overrightarrow{AC} = 8$, and angle $∠BAC = \theta$, with $a=4$.
(1) Find the maximum value of $bc$.
(2) Determine the range of values of the function $f(\theta) = \sqrt{3}\sin{2\theta} + \cos{2\theta} - 1$.

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