
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  $ABC$  be a triangle with incenter  $I$  and  $AB = 1400$ ,  $AC = 1800$ ,  $BC = 2014$ .  The circle centered at  $I$  passing through  $A$  intersects line  $BC$  at two points  $X$  and  $Y$ . Compute the length  $XY$ .

*Proposed by Evan Chen*

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