
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
The intervals on which the function \( y = \left\{
\begin{array}{cc}
2x + 3, & x \leq 0, \\
x + 3, & 0 < x \leq 1, \\
-x + 5, & x > 1
\end{array}
\right. \) is monotonically increasing.

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