
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
For the quadratic function $y=x^2+2x-3$,  
(1) Indicate the direction of the graph's opening, the equation of the axis of symmetry, and the coordinates of the vertex;  
(2) Analyze the monotonicity of the function;  
(3) When $x \in [-2, 3]$, find the range of the function.

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