
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 a similar setup, two isosceles triangles $\triangle ABC$ and $\triangle DEF$ support a horizontal beam, where $\triangle ABC$ is located to the left of $\triangle DEF$. Given that $\angle BAC = 30^\circ$ and $\angle EDF = 40^\circ$, assume that triangles have equal heights. What is the sum of $\angle DAC$ and $\angle ADE$?

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