
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
Suppose we have two sets, A and B, defined as follows:
A = {x | 1 < x < 2},
B = {x | 3/2 < x < 4}.
1. Find the union of sets A and B (A ∪ B).
2. Let there be a set P = {x | a < x < a + 2}. If P is a subset of the union of A and B (P ⊆ A ∪ B), determine the range of the real number a.

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