
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 proposition $p$: $\exists x_{0} \in [0,2]$, $\log _{2}(x_{0}+2) < 2m$; and proposition $q$: the angle between vector $\overrightarrow{a}=(1,m)$ and vector $\overrightarrow{b}=(1,-3m)$ is acute.
(I) Find the range of values for the real number $m$ if proposition $q$ is true;
(II) Find the range of values for the real number $m$ if $(\lnot p) \land q$ is true.

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