
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 the set of real numbers $\mathbb{R}$, an operation $\otimes$ is defined as follows: $x \otimes y = x(1 - y)$. If there exist $x_1$ and $x_2$ ($x_1 \neq x_2$) such that the equation $1 \otimes (2k - 3 - kx) = 1 + \sqrt{4 - x^2}$ holds, find the range of the real number $k$.

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