
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
Let \( m > 1 \). Under the constraints
\[
\begin{cases}
y \geqslant x, \\
y \leqslant mx, \\
x + y \leqslant 1
\end{cases}
\]

the maximum value of the objective function \( z = x + my \) is less than 2. Determine the range of \( m \).

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