
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 trapezoid $ABCD$, where bases $AD$ and $BC$ are parallel, $AD = 90$ units and $BC = 40$ units. The non-parallel sides $AB$ and $CD$ meet at angle $\alpha = 45^\circ$ at vertex $A$. Given $AB = 30$ units, calculate the perimeter of trapezoid $ABCD$.

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