
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
In the convex quadrilateral \(ABCD\), the length of the segment connecting the midpoints of sides \(AB\) and \(CD\) is 1. The lines \(BC\) and \(AD\) are perpendicular. Find the length of the segment connecting the midpoints of the diagonals \(AC\) and \(BD\).

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