
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 the universal set U = R, the set M = {x | 3a - 1 < x < 2a, a ∈ R}, and N = {x | -1 < x < 3}, find the set of values for the real number a such that N is a subset of the complement of M in U (N ⊆ ∁<sub>U</sub>M).

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