
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 propositions $p$: the equation $x^2 - 2x + m = 0$ has real roots, and $q$: $m \in [-1, 5]$.  
(1) When proposition $p$ is true, find the range of values that the real number $m$ can take.  
(2) If proposition $p \land q$ is false, and $p \lor q$ is true, find the range of values for the real number $m$.

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