
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
Consider the sequence

$$
\begin{aligned}
x_{1} & =19, \\
x_{2} & =95, \\
x_{n+2} & =\operatorname{lcm}\left(x_{n+1}, x_{n}\right)+x_{n},
\end{aligned}
$$

for \(n > 1\), where \(\operatorname{lcm}(a, b)\) means the least common multiple of \(a\) and \(b\). Find the greatest common divisor of \(x_{1995}\) and \(x_{1996}\).

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