
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 $P=\{x|a-4 < x < a+4\}$, $Q=\{x|x^{2}-4x+3 < 0\}$, and $x \in P$ is a necessary condition for $x \in Q$, find the range of the real number $a$.

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