
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 $$f(x)= \begin{cases} -x^{3}+x^{2}+bx+c & (x<1) \\ a\ln{x} & (x\geq1)\end{cases}$$ whose graph passes through the point $(-1, 2)$, and the tangent line at the point $(-1, f(-1))$ is perpendicular to the line $x-5y+1=0$.  
(Ⅰ) Find the values of the real numbers $b$ and $c$;  
(Ⅱ) Find the maximum value of $f(x)$ on the interval $[-1, e]$ ($e$ is the base of the natural logarithm).

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