
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 vectors $m = (a, b)$, $n = (c, d)$, and $p = (x, y)$, define a new operation $m \otimes n = (ac + bd, ad + bc)$, where the operations on the right side of the equation are the usual addition and multiplication. If for any vector $m$, it holds that $m \otimes p = m$, then the vector $p = \_\_\_\_\_\_\_\_$.

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