
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
Given $U = \{(x, y) : x \in \{0, 1, 2, 3, 4, 5\}, y \in \{0, 1, 2, 3, 4\}\}$, let $V$ be the set of all right triangles whose vertices are in $U$. For each right triangle $v = \triangle{DEF}$ with vertices $D$, $E$, and $F$ in counter-clockwise order and a right angle at $D$, let $g(v) = \tan(\angle EFD)$. Calculate $\prod_{v\in V} g(v)$.

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