
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
Consider a circle centered at  $O$ . Parallel chords  $AB$  of length  $8$  and  $CD$  of length  $10$  are of distance  $2$  apart such that  $AC < AD$ . We can write  $\tan \angle BOD =\frac{a}{b}$  , where  $a, b$  are positive integers such that gcd  $(a, b) = 1$ . Compute  $a + b$ .

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