
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
The triangle  $K_2$  has as its vertices the feet of the altitudes of a non-right triangle  $K_1$ . Find all possibilities for the sizes of the angles of  $K_1$  for which the triangles  $K_1$  and  $K_2$  are similar.

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