
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 propositions:  
p: For all $x \in \mathbb{R}$, $\sqrt{3}\sin x + \cos x > m$,  
q: There exists an $x \in \mathbb{R}$ such that $x^2 + mx + 1 \leq 0$.  
If the proposition “$p \vee q$” (p OR q) is true, and “$p \wedge q$” (p AND q) is false, determine the range of the real number $m$.

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