
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 acute triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\frac{ac}{b^2 - a^2 - c^2} = \frac{\sin A \cos A}{\cos(A + C)}$.
(1) Find angle $A$;
(2) If $a = \sqrt{2}$, find the range of $bc$.

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