
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 sequence $\left\{a_{n}\right\}$ satisfying:
$$
a_{0}=\sqrt{6}, \quad a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}} \text {, }
$$

where $[a]$ denotes the greatest integer less than or equal to the real number $a$, and $\{a\}=a-[a]$. Determine the value of $a_{2020}$.

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