
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
If two linear functions $y=k_1x+b_1$ ($k_1\neq 0$) and $y=k_2x+b_2$ ($k_2\neq 0$), then the function $y=(k_1+k_2)x+b_1b_2$ is called the composite function of these two functions.  
(1) The composite function of the linear functions $y=3x+2$ and $y=-4x+3$ is; if the composite function of the linear functions $y=ax-2$ and $y=-x+b$ is $y=3x+2$, then $a=$, $b=$.  
(2) Given that the graph of the composite function of the linear functions $y=-x+b$ and $y=kx-3$ passes through the first, second, and fourth quadrants, find the conditions that the constants $k$ and $b$ must satisfy;  
(3) Given that the linear functions $y=-2x+m$ and $y=3mx-6$, regardless of the value, the composite function always passes through a fixed point with coordinates.

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