
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 the following propositions:
Proposition 1: The point (1,1) is an intersection point of the line y=x and the hyperbola y= $\frac {1}{x}$;
Proposition 2: The point (2,4) is an intersection point of the line y=2x and the hyperbola y= $\frac {8}{x}$;
Proposition 3: The point (3,9) is an intersection point of the line y=3x and the hyperbola y= $\frac {27}{x}$;
...
Observe the above propositions and conjecture Proposition n (n is a positive integer): ___.

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