
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
Identify the maximum value of the parameter \( a \) for which the system of equations

\[
\left\{\begin{array}{l}
y = 1 - \sqrt{x} \\
a - 2(a - y)^2 = \sqrt{x}
\end{array}\right.
\]

has a unique solution.

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