
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
Define a set \( S = \{(x,y) : x \in \{-2, -1, 0, 1, 2\}, y \in \{-3, -2, -1, 0, 1, 2, 3\}\} \) and exclude the point \( (0,2) \). Let \( T \) be the set of all right triangles with vertices from \( S \). For each right triangle \( \triangle ABC \) with vertices \( A \), \( B \), and \( C \) in counter-clockwise order and right angle at \( A \), let \( f(t) = \tan(\angle CBA) \). Calculate \(\prod_{t \in T} f(t)\).
A) 0.5
B) 1
C) 1.5
D) 2

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