
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
On the complex plane, points \( A \) and \( B \) correspond to the complex numbers \( z_1 = 2 \) and \( z_2 = -3 \) respectively. 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 point \( P \) moves on the upper semicircle (excluding the two endpoints) with the center at the origin and radius 1, find the minimum value of \( \varphi \).

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