
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 $\overrightarrow {m}=(1，-2)$ and $\overrightarrow {n}=(1，\lambda)$.  
(I) If the projection of $\overrightarrow {n}$ on $\overrightarrow {m}$ is $\sqrt {5}$, find the value of $\lambda$;  
(II) Proposition P: The angle between vector $\overrightarrow {m}$ and $\overrightarrow {n}$ is acute;  
Proposition Q: $\overrightarrow {a}=2 \overrightarrow {b}$, where vector $\overrightarrow {a}=(\lambda+2，\lambda^{2}-\cos^{2}\alpha)$, $\overrightarrow {b}=(\frac {1}{2}\lambda+1， \frac {\lambda}{2}+\sin\alpha)$ ($\lambda，\alpha\in\mathbb{R}$). If "P or Q" is true, and "P and Q" is false, find the range of values for $\lambda$.

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