
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, 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 along the upper semicircle centered at the origin with radius 1 (excluding the endpoints), find the minimum value of \(\varphi\).

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