
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: "The range of the function $y=\log(x^2+2ax+2-a)$ is $\mathbb{R}$", and q: "$\forall x \in [0,1], x^2+2x+a \geq 0$"  
(1) If proposition p is true, find the range of the real number $a$.  
(2) If the proposition "p $\lor$ q" is true, find the range of the real number $a$.

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