
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
Let  $ABCD$  be a trapezium with  $AB// DC, AB = b, AD = a ,a<b$  and  $O$  the intersection point of the diagonals. Let  $S$  be the area of the trapezium  $ABCD$ . Suppose the area of  $\vartriangle DOC$  is  $2S/9$ . Find the value of  $a/b$ .

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