
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
6 points  $A,\ B,\ C,\ D,\ E,\ F$  are on a circle in this order and the segments  $AD,\ BE,\ CF$  intersect at one point.
If  $AB=1,\ BC=2,\ CD=3,\ DE=4,\ EF=5$ , then find the length of the segment  $FA$ .

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