
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
Higher Secondary P2

Let  $g$  be a function from the set of ordered pairs of real numbers to the same set such that  $g(x, y)=-g(y, x)$  for all real numbers  $x$  and  $y$ . Find a real number  $r$  such that  $g(x, x)=r$  for all real numbers  $x$ .

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