
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
If the function $f(x)=\frac{x^3}{3}-\frac{a}{2}x^2+x+1$ has an extreme point in the interval $\left(\frac{1}{2},3\right)$, then the range of the real number $a$ is $\boxed{\text{C: }(2,\frac{10}{3})}$.

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