
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 $f\left( x \right)=2\ln x-3{{x}^{2}}-11x$.

(1) Find the equation of the tangent line to the curve $y=f\left( x \right)$ at the point $\left( 1,f\left( 1 \right) \right)$.

(2) If $\forall x\in \left( 0,+\infty \right)$, $f\left( x \right)\leqslant \left( a-3 \right){{x}^{2}}+\left( 2a-13 \right)x+1$ always holds, find the minimum value of the integer $a$.

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