
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 $(x,y)$ subject to the constraints
\begin{cases} 
& x-3\leqslant 0 \\
& y-a\leqslant 0 \\
& x+y\geqslant 0 \\
\end{cases}
and the objective function $z=2x+y$ has a maximum value of $10$, determine the value of $a$.

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