
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 real number $x > 1$, and real numbers $x$, $y$ satisfy the system of inequalities $\begin{cases}y \geqslant x \\ y \leqslant 2x \\ x+y \leqslant 1\end{cases}$. If the maximum value of the objective function $z=x+my$ equals $3$, then the value of $m$ is $\boxed{\text{(C) } 4}$.

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