
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 \( A = \{ x \mid |x| (x^2 - 4x + 3) < 0, x \in \mathbb{R} \} \) and \( B = \{ x \mid 2^{1-x} + a \leq 0, x^2 - 2(a+7)x + 5 \leq 0, x \in \mathbb{R} \} \). If \( A \subseteq B \), find the range of the real number \( a \).

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