
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
Point  $A,B$  are marked on the right branch of the hyperbola   $y=\frac{1}{x},x>0$ . The straight line  $l$  passing through the origin  $O$  is perpendicular to  $AB$  and meets   $AB$  and given branch of the hyperbola at points  $D$  and  $C$  respectively. The circle through  $A,B,C$  meets  $l$  at  $F$ . 
Find  $OD:CF$  

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