
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
The domain of \\(f(x)= \sqrt { \frac {2-x}{x-1}}\\) is \\(A\\), and the solution set of the inequality \\(2^{2ax} < 2^{a+x}\\) with respect to \\(x\\) is \\(B\\). Find the range of real numbers \\(a\\) for which \\(A \cap B = A\\).

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