
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 $xoy$, given the line $l: 8x+6y+1=0$, and circles $C_1: x^2+y^2+8x-2y+13=0$, $C_2: x^2+y^2+8tx-8y+16t+12=0$.

(1) When $t=-1$, determine the positional relationship between circle $C_1$ and circle $C_2$, and explain the reason;

(2) If circle $C_1$ and circle $C_2$ are symmetric about line $l$, find the value of $t$.

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