
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 $C_{1}$ is defined by the equation $x^{2}+y^{2}-4x-8y+19=0$. This circle is symmetric with respect to the line $l$ defined by the equation $x+2y-a=0$. Determine the value of the real number $a$.

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