
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 functions $f(x) = x\ln(x)$ and $g(x) = (-x^2 + ax - 3)e^x$ (where $a$ is a real number). When $a = 5$, find the equation of the tangent line to the function $y = g(x)$ at $x = 1$.

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