
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 proposition $p$: the inequality $x-x^{2}\leqslant a$ holds for all $x\geqslant 1$, and the proposition $q$: the equation $x^{2}-ax+1=0$ has real roots.

1. If $\lnot p$ is a false proposition, find the range of values for the real number $a$.
2. If "$p\land q$" is a false proposition, and "$p\lor q$" is a true proposition, find the range of values for the real number $a$.

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