
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
Find all values of \( a \) for which the system 

\[
\left\{
\begin{array}{l}
x^{2} + 4y^{2} = 1 \\
x + 2y = a
\end{array}
\right.
\]

has a unique solution. If necessary, round your answer to two decimal places. If there are no solutions, answer with 0.

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