
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 quadrilateral \(ABCD\), \(\angle DAB = \angle DBC = 90^\circ\). Additionally, \(DB = a\) and \(DC = b\).

Find the distance between the centers of two circles, one passing through points \(D, A, B\), and the other passing through points \(B, C, D\).

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