
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 a function $f(x)= \frac{1}{3}x^{3}- \frac{t}{2}x^{2}+kx$ $(t>0，k>0)$, it achieves a local maximum at $x=a$ and a local minimum at $x=b$. Moreover, the numbers $a$, $b$, and $-2$ can be reordered to form both an arithmetic sequence and a geometric sequence. Find the value of $t$.

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