
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 graph of the quadratic function $y=(x-h)^{2}+k$ (where $h$ and $k$ are constants) passes through three points $P_{1}(-3,y_{1})$, $P_{2}(-1,y_{2})$, and $P_{3}(1,y_{3})$. If $y_{2} \lt y_{1} \lt y_{3}$, then the range of $h$ is ____.

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