
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 the set \\(A = \{x | f(x) = \lg(x - 1) + \sqrt{2 - x}\}\), and the set \\(B = \{y | y = 2^x + a, x \leqslant 0\}\):
\\((1)\\) If \\(a = \frac{3}{2}\), find \\(A \cup B\);
\\((2)\\) If \\(A \cap B = \varnothing\), find the range of the real number \\(a\).

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