
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
 $AD$  is the altitude on side  $BC$  of triangle  $ABC$ . If  $BC+AD-AB-AC = 0$ , find the range of  $\angle BAC$ .

*Alternative formulation.* Let  $AD$  be the altitude of triangle  $ABC$  to the side  $BC$ . If  $BC+AD=AB+AC$ , then find the range of  $\angle{A}$ .

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