
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 inequalities
\[
\begin{cases}
x - 4y + 3 \leq 0, \\
3x + 5y - 25 \leq 0, \\
x \geq 1,
\end{cases}
\]
and the objective function \( z = kx + y \) has a maximum value of 12 and a minimum value of 3, determine the value of the real number \( k \).

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