
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 line $l: kx-y-k+1=0$ and the graph of the function $f(x)= \begin{cases} x^{3}-3x^{2}+2x+1, & x\leqslant 2\\ ax-2a+1, & x > 2 \end{cases}$ intersect at three points, with their $x$-coordinates being $x_{1}$, $x_{2}$, and $x_{3}$. If for any $0 < k < 3$, $x_{1}+x_{2}+x_{3} < 3$ always holds, then the range of the real number $a$ is \_\_\_\_\_\_.

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