
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 system $xOy$, two tangents are drawn from point $P(-5,a)$ to the circle $x^{2}+y^{2}-2ax+2y-1=0$. The points of tangency are $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$, and it is 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