
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
Let $n$ be the integer such that $0 \le n < 19$ and $5n \equiv 1 \pmod{19}$. What is the value of $\left(3^n\right)^2 - 3 \pmod{19}$? Express your answer as an integer from $0$ to $18$, inclusive.

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