
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 $p$: "For all $k \in \mathbb{R}$, the line $y=kx+1$ has two distinct common points with the ellipse $\frac{x^2}{1} + \frac{y^2}{a} = 1$"; $q$: "There exists $x_0 \in \mathbb{R}$, such that the inequality $4^{x_0} - 2^{x_0} - a \leqslant 0$ holds"; If "$p$ and $q$" is a false statement, and "$p$ or $q$" is a true statement, find the range of the real number $a$.

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