
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 trapezoid $ABCD$ has bases $AD$ and $BC$. If $BC = 60$ units, and altitudes from $B$ and $C$ to line $AD$ divide it into segments of lengths $AP = 20$ units and $DQ = 19$ units, with the length of the altitude itself being $30$ units, what is the perimeter of trapezoid $ABCD$?
**A)** $\sqrt{1300} + 159$
**B)** $\sqrt{1261} + 159$
**C)** $\sqrt{1300} + \sqrt{1261} + 159$
**D)** $259$
**E)** $\sqrt{1300} + 60 + \sqrt{1261}$

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