
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 point A(1,3) and point B(3,1), point C is the intersection of lines $l_1$: $3x - 2y + 3 = 0$ and $l_2$: $2x - y + 2 = 0$.
(1) Determine the coordinates of intersection point C for lines $l_1$ and $l_2$;
(2) Calculate the area of triangle ABC.

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