
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 $\left\{x_{n}\right\}: 1,3,3,3,5,5,5,5,5, \cdots$ is formed by arranging all positive odd numbers in increasing order, and each odd number $k$ appears consecutively $k$ times, where $k=1,3,5, \cdots$. If the general term formula of this sequence is given by $x_{n}=a[\sqrt{b n+c}]+d$, find the value of $a+b+c+d$.

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