
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

Specify the values of the parameter \( a \) for which the equation

\[ \frac{2 - 2a(x + 1)}{|x| - x} = \sqrt{1 - a - ax} \]

has at least one solution. Find the solutions of this equation for all the obtained values of the parameter \( a \).

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