
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 the proposition $p: \{m|2^{m} > \sqrt{2}, m \in \mathbb{R}\}$ and the proposition $q$: the equation $x^2 - 2x + m^2 = 0$ has two different real roots with respect to $x$.
(1) If $p \land q$ is true, find the range of values for the real number $m$;
(2) If $p \vee q$ is true, $p \land q$ is false, find the range of values for the real number $m$.

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