
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 $f(x)= \frac {1}{3}x^{3}- \frac {1}{2}x^{2}+1$, where $x\in\mathbb{R}$.

$(1)$ Find the maximum and minimum values of the function $f(x)$;  
$(2)$ Find the equation of the tangent line to the graph of the function at the point $(\frac {3}{2},1)$;  
$(3)$ Find the area of the closed shape formed by the graph of the function $f(x)= \frac {1}{3}x^{3}- \frac {1}{2}x^{2}+1$ and the line $y=1$.

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