
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 system of equations in $x, y$:
$$
\begin{cases}
ax+y-1=0 \\
4x+ay-2=0
\end{cases}
$$
If there are infinitely many solutions, then the value of the real number $a$ is $\boxed{?}$.

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