
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 two circles \\(x^{2}+y^{2}-4x+2y+5-a^{2}=0\\) and \\(x^{2}+y^{2}-(2b-10)x-2by+2b^{2}-10b+16=0\\) intersect at points \\(A(x_{1},y_{1})\\) and \\(B(x_{2},y_{2})\\), and it satisfies \\(x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2}\\), then \\(b=\)_______.

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