
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
[ $XYZ$ ] denotes the area of  $\triangle XYZ$ We have a  $\triangle ABC$ , $BC=6,CA=7,AB=8$ (1)If  $O$  is the circumcenter of  $\triangle ABC$ , find [ $OBC$ ]:[ $OCA$ ]:[ $OAB$ ]
(2)If  $H$  is the orthocenter of  $\triangle ABC$ , find [ $HBC$ ]:[ $HCA$ ]:[ $HAB$ ]

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