
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
Consider the set $S=\{(x,y): x\in \{1,2,3,4,5\}, y\in \{1,2,3,4,5,6\}\}$. Let $T$ be the set of all right triangles whose vertices are points in $S$. For each right triangle $t=\triangle{ABC}$ with vertices $A$, $B$, and $C$ in counter-clockwise order, and right angle at $A$, define $f(t)=\tan(\angle{CBA})\cdot \tan(\angle{ACB})$. Compute the product $\prod_{t\in T} f(t)$.

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