
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
Let  $c$  be a positive integer. Consider the sequence  $x_1,x_2,\ldots$  which satisfies  $x_1=c$  and, for  $n\ge 2$ ,
\[x_n=x_{n-1}+\left\lfloor\frac{2x_{n-1}-(n+2)}{n}\right\rfloor+1\]
where  $\lfloor x\rfloor$  denotes the largest integer not greater than  $x$ . Determine an expression for  $x_n$  in terms of  $n$  and  $c$ . 

*Huang Yumin*

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