
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
Let $P$: "The solution set of the inequality about $x$, $x^{2}-ax+a+ \frac {5}{4} > 0$, is $\mathbb{R}$," and $Q$: "The equation $\frac {x^{2}}{4a+7}+ \frac {y^{2}}{a-3}=1$ represents a hyperbola."  
(1) If Q is true, find the range of values for the real number $a$;  
(2) If $P \land Q$ is false and $P \lor Q$ is true, find the range of values for the real number $a$.

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