
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 $f(x)=(x^{3}-6x^{2}+3x+t)⋅e^{x}$, where $t∈R$.
(1) When $t=1$, find the equation of the tangent line to the function $y=f(x)$ at $x=0$;
(2) If the function $y=f(x)$ has three distinct extreme points, find the range of $t$;
(3) If there exists a real number $t∈[0,2]$, such that for any $x∈[1,m]$, the inequality $f(x)≤x$ always holds, find the maximum value of the positive integer $m$.

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