
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
 $f:R->R$  such that :  $f(1)=1$  and for any  $x\in R$  
i)  $f(x+5)\geq f(x)+5$ ii) $f(x+1)\leq f(x)+1$ If  $g(x)=f(x)+1-x$  find g(2016)

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