
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 $A=\{x|x^2-4x+3<0, x\in \mathbb{R}\}$, and $B=\{x|2^{1-x}+a\leq0, x^2-2(a+7)x+5\leq0, x\in \mathbb{R}\}$. If $A \subseteq B$, then the range of the real number $a$ is \_\_\_\_\_\_\_\_\_\_\_\_.

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