
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 $a_{1}=1996$,
$$
a_{k}=\left[\sqrt{a_{1}+a_{2}+\cdots+a_{k-1}}\right], \quad k=2,3, \cdots
$$

where $[x]$ denotes the greatest integer less than or equal to $x$. Find $a_{1966}$.

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