
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
A regular 15-gon is inscribed in a circle of radius 15. The sum of the lengths of all sides and diagonals of the 15-gon can be written in the form
\[ a + b \sqrt{2} + c \sqrt{3} + d \sqrt{5}, \]
where $a$, $b$, $c$, and $d$ are positive integers. Find $a+b+c+d$.

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