
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 propositions $p$ and $q$:
- Proposition $p$: "The equation $x^{2}-2ax+y^{2}+2a^{2}-5a+4=0$ ($a\in\mathbb{R}$) represents a circle."
- Proposition $q$: "For all $x\in\mathbb{R}$, $x^{2}+(a-1)x+1 > 0$ ($a\in\mathbb{R}$) holds."
  1. If proposition $p$ is true, find the range of values for $a$.
  2. If proposition $p \land q$ is true, find the range of values for $a$.

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