
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
In a convex quadrilateral  $ABCD$ ,  $\angle ABC = 90^o$  ,  $\angle BAC = \angle  CAD$ ,  $AC = AD, DH$  is the alltitude of the triangle  $ACD$ . In what ratio does the line  $BH$  divide the segment  $CD$ ?

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