
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 \( a > 0 \) and \( x, y \) satisfying the constraints \(\left\{\begin{array}{l}x \geqslant 1, \\ x+y \leqslant 3, \\ y \geqslant a(x-3) .\end{array}\right.\) and if the minimum value of \( z = 2x + y \) is 1, what is the value of \( a \)?

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