
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 function $f(x) = \log_{2}(x^2 - 2ax + 16)$ has a minimum value.
- Proposition $q$: The quadratic equation $2x^2 - (2a - 2)x + 3a - 7 = 0$ has real roots with respect to $x$.
Determine the range of the real number $a$ that makes the compound proposition $p \land q$ true.

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