
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 $f(x) = ax^3 + x + 1$, the tangent line at the point $(1, f(1))$ passes through the point $(3, 7)$.
(Ⅰ) Find the analytical expression of the function $f(x)$;
(Ⅱ) Calculate the value of $f(-4) + f(-3) + \ldots + f(3) + f(4)$.

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