
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 $f(x) = x^3 - 3ax + b$ $(a, b \in \mathbb{R})$ attains an extremum of $1$ at $x = -1$.

(Ⅰ) Find the values of $a$ and $b$;

(Ⅱ) Find the equation of the tangent line to the function $g(x) = f(x) + e^{2x-1}$ at $x = 1$.

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