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

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