
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 a linear function $y=kx+b$ passes through points A(2, 4), B(3, 5), and C(-4, a), and an inverse proportion function also passes through point C,  
(1) Find the equation of the linear function;  
(2) Find the area of the triangle formed by the linear function and the coordinate axes;  
(3) Find the equation of the inverse proportion function.

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