
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 function  $f(x,y)$ , defined on the set of all non-negative integers, satisfies 
(i)  $f(0,y)=y+1$ 
(ii)  $f(x+1,0)=f(x,1)$ 
(iii)  $f(x+1,y+1)=f(x,f(x+1,y))$ 
Find f(3,2005), f(4,2005)

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