
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 that point $P(x,y)$ moves within the region represented by the system of inequalities $\begin{cases} 2x-y+a \geqslant 0 \ 3x+y-3 \leqslant 0 \end{cases}$ (where $a$ is a constant), and the maximum value of $z=4x+3y$ is $8$, find the value of $a$.

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