
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
The sequence is defined recursively:

\[ x_{0} = 0, \quad x_{n+1} = \frac{(n^2 + n + 1) x_{n} + 1}{n^2 + n + 1 - x_{n}}. \]

Find \( x_{8453} \).

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