
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 an acute isosceles triangle $ABC$, inscribed in a circle, tangents are drawn through points $B$ and $C$, meeting at point $D$ outside the circle. Given that $\angle ABC = \angle ACB = 3 \angle D$ and if $\angle BAC = l \cdot \pi$ with $l$ unknown, determine the value of $l$.

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