
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
Definition: In a function, we call a pair of linear functions in terms of $x$, $y=mx+n$ and $y=nx+m$, a set of symmetric functions, such as $y=-2x+3$ and $y=3x-2$ are a set of symmetric functions. Then the coordinates of the intersection point of the symmetric function of $y=-6x+4$ with the $y$-axis are ______.

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