
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 circle \(O\), \(Q\) is the midpoint of radius \(OX\). Through \(Q\), draw \(AB \perp XY\), and use \(AB\) as the diameter to draw a semicircle intersecting \(XY\) at \(M\). \(AM\) and \(BM\) intersect circle \(O\) at \(C\) and \(D\) respectively. Connect \(AD\). Find the length of \(AD\) in terms of the radius of circle \(O\).

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