
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 lengths of the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\overrightarrow{AB} \cdot \overrightarrow{AC} = 8$, $\angle BAC = \theta$, $a = 4$.

1. Find the maximum value of $bc$.
2. Find the range 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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