
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 parallelogram  $ABCD,$  let  $O$  be the intersection of diagonals  $\overline{AC}$  and  $\overline{BD}.$   Angles  $CAB$  and  $DBC$  are each twice as large as angle  $DBA,$  and angle  $ACB$  is  $r$  times as large as angle  $AOB.$   Find the greatest integer that does not exceed  $1000r.$ 

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