
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 $x^2+y^2-2ax+2y-1=0$, and the points of tangency are $M(x_1, y_1)$ and $N(x_2, y_2)$, respectively. If $$\frac {y_{2}-y_{1}}{x_{2}-x_{1}} + \frac {x_{1}+x_{2}-2}{y_{1}+y_{2}} = 0$$, then the value of the real number $a$ is \_\_\_\_\_\_.

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