
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 the cartesian coordinate plane $(xOy)$, a circle $(x^{2}+y^{2}-2ax+2y-1=0)$ passes through the point $P(-5,a)$. The circle has two tangent lines intersecting the circle at points $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$. Given that $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}+\frac{x_{1}+x_{2}-2}{y_{1}+y_{2}}=0$, find the value of the real number $a$.

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