
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 sets \( A = \{ x \mid (x + 3)(x - 6) \geq 0 \} \), and \( B = \left\{ x \bigg| \frac{x+2}{x-14} < 0 \right\} \).
1. Find \( A \cap \complement_R B \);
2. Let \( E = \{ x \mid 2a < x < a + 1 \} \) with \( a \) being a real number. If \( E \subseteq B \), determine the range of possible values for the real number \( a \).

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