
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 real numbers $x$ and $y$ satisfy the following conditions:
\[
\begin{cases}
\begin{matrix}
x+3y+5 \geqslant 0 \\
x+y-1 \leqslant 0
\end{matrix} \\
x+a \geqslant 0
\end{cases}
\]
If the minimum value of $z=x+2y$ is $-4$, then the value of the real number $a$ is _______.

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