
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
Given a linear function whose graph passes through the points (3,5) and (-4,-9),
(1) Find the equation of the linear function.
(2) Determine the coordinates of the intersection points with the coordinate axes.
(3) Calculate the area of the triangle formed by the graph and the coordinate axes.
(4) If the point (a,2) lies on the graph, find the value of a.

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