
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 \\(a \in \mathbb{R}\\), \\(p\\): The equation \\(x^{2}-2x+a=0\\) has two distinct real roots; \\(q\\): The equation \\(\dfrac{x^{2}}{a-3} + \dfrac{y^{2}}{a+1}=1\\) represents a hyperbola. If \\(p \lor q\\) is false, find the range of the real number \\(a\\).

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