
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 the function $f(x)=3\ln x-\frac{1}{2}x^{2}+2x$.
(1) Determine the monotonic intervals of the function $f(x)$, and indicate its monotonicity;
(2) Find the area of the triangle formed by the tangent line to the graph of the function $y=f(x)$ at the point $x=1$ and the two coordinate axes.

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