
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
In the Cartesian coordinate plane \( xOy \), point \( P \) is a moving point on the ellipse \(\frac{y^{2}}{4}+\frac{x^{2}}{3}=1\). The coordinates of points \( A \) and \( B \) are \((1,1)\) and \((0,-1)\), respectively. What is the maximum value of \( |PA| + |PB| \)?

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