
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
Let  $ AD $  be the bisector of a triangle  $ ABC $    $ (D \in BC) $  such that  $ AB + AD = CD $  and  $ AC + AD = BC $ . Determine the measure of the angles of  $ \vartriangle ABC $ 

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