
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
On a circumference, points  $A$  and  $B$  are on opposite arcs of diameter  $CD$ . Line segments  $CE$  and  $DF$  are perpendicular to  $AB$  such that  $A-E-F-B$  (i.e.,  $A$ ,  $E$ ,  $F$  and  $B$  are collinear on this order). Knowing  $AE=1$ , find the length of  $BF$ .

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