
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 $f(x) = 2\ln x - 3x^2 - 11x$.
1. Find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$.
2. If the inequality $f(x) \leqslant (a-3)x^2 + (2a-13)x + 1$ holds for all $x$, find the minimum value of the integer $a$.

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