
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
If the non-empty set \(A = \{x \mid 2a+1 \leq x \leq 3a-5\}\) and \(B = \{x \mid 3 \leq x \leq 22\}\), determine the set of all real numbers \(a\) such that \(A \subseteq A \cap B\).

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