
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
Given the standard equation of circle C as (x-2)<sup>2</sup>+(y-3)<sup>2</sup>=1, the line AM is tangent to circle C at point M. If the coordinates of point A are (a, b), and point A satisfies |AM|=|AO| (where point O is the origin of the coordinates), then a + $\frac {3}{2}$b = _____ .

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