
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
Two circles with radii $\sqrt{5}$ and $\sqrt{2}$ intersect at point $A$. The distance between the centers of the circles is 3. A line through point $A$ intersects the circles at points $B$ and $C$ such that $A B = A C$ (point $B$ does not coincide with $C$). Find $A B$.

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