
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 that $A$ is an internal angle of acute triangle $ABC$, and $\sin A - 2\cos A = a (a \in \mathbb{R})$.
(I) If $a = -1$, find the value of $\tan A$;
(II) If $a < 0$, and the function $f(x) = (\sin A) \cdot x^2 - (2\cos A) \cdot x + 1$ is an increasing function in the interval $[1, 2]$, find the range of $\sin^2 A - \sin A \cdot \cos A$.

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