
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
(The full score for this question is 14 points)  
Given proposition p: The function $y = \log_a x$ is increasing on the interval $(0, +\infty)$; proposition q: The equation $x^2 - 2ax + 4 = 0$ has real roots. If $p \land q$ is true, find the range of real numbers $a$.

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