
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
Given four distinct points $A, B, C$, and $D$ in space, there exists isometry in space that swaps $A$ and $B$, and leaves $C$ and $D$ unchanged. Additionally, there is an isometry that maps $A$ to $B$, $B$ to $C$, $C$ to $D$, and $D$ to $A$. What is the measure of angle $ABC$? And what is the measure of angle $DAC$?

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