
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 \( A=\{ x \mid x^2 - 4x + 3 < 0, x \in \mathbf{R} \} \) and \( B=\{ x \mid 2^{1} + a \leq 0, x^2 - 2(a + 7)x + 5 \leq 0, x \in \mathbf{R} \} \), if \( A \subseteq B \), then the range of the real number \( a \) is \(\qquad\).

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