
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
The graph of the cubic function $f(x)=ax^{3}- \frac {3}{2}x^{2}+2x+1$ has a tangent line at the point $(1, f(1))$ that is parallel to the x-axis. Find the minimum value of $f(x)$ on the interval $(1,3)$.

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