
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
(i) Find the angles of  $\triangle ABC$  if the length of the altitude through  $B$  is equal to the length of the median through  $C$  and the length of the altitude through  $C$  is equal to the length of the median through  $B$ .

(ii) Find all possible values of  $\angle ABC$  of  $\triangle ABC$  if the length of the altitude through  $A$  is equal to the length of the median through  $C$  and the length of the altitude through  $C$  is equal to the length of the median through  $B$ .

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