
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 following linear programming problem: Find the maximum and minimum values of $z=3x+5y$ subject to the following constraints:
$$
\begin{aligned}
&6x+3y \leq 15, \\
&y \leq x+1, \\
&x-5y \leq 3.
\end{aligned}
$$
To ensure that the objective function $z$ has only a minimum value without a maximum value, devise a method to modify one of the constraints (still consisting of three inequalities). The result is ________.

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