
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
Points  $A,B,C,D$  have been marked on checkered paper (see fig.). Find the tangent of the angle  $ABD$ . 
![Image](https://cdn.artofproblemsolving.com/attachments/6/1/eeb98ccdee801361f9f66b8f6b2da4714e659f.png)

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