
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 $\overrightarrow{m}=(a,b)$, $\overrightarrow{n}=(c,d)$, $\overrightarrow{p}=(x,y)$, define a new operation $\overrightarrow{m}\* \overrightarrow{n}=(ac+bd,ad+bc)$, where the right side of the equation is the usual addition and multiplication operations. If for any vector $\overrightarrow{m}$ we have $\overrightarrow{m}\* \overrightarrow{p}= \overrightarrow{m}$ holds, then vector $\overrightarrow{p}$ is $(x,y)$.

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