
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
Let the mapping $f: x \rightarrow -x^2 + 2x$ be a mapping from the set of real numbers $M$ to the set of real numbers $N$. If for a real number $P \in N$, there does not exist a pre-image in $M$, then the range of values for $P$ is ____ . (Express the set or interval)

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