
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 complex plane, the points \( A \) and \( B \) correspond to the complex numbers \( z_{1} = 2 \) and \( z_{2} = -3 \), respectively. The point \( P \) corresponds to the complex number \( z \), and the principal value of the argument of \( \frac{z-z_{1}}{z-z_{2}} \) is \( \varphi \). When the point \( P \) is moving on the upper semicircle with radius 1 centered at the origin (excluding the endpoints), find the minimum value of \( \varphi \).

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