
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 conditions $p$ and $q$: condition $p$ states that there exists an $m \in [-1, 1]$ such that the inequality $a^2 - 5a + 5 \geq m + 2$ holds; condition $q$ states that the equation $x^2 + ax + 2 = 0$ has two negative real roots. If $p \vee q$ is true and $p \wedge q$ is false, find the range of values for the real number $a$.

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