
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
If the moving straight line $x=t\left(t\in R\right)$ intersects the graphs of the functions $f(x)=\cos^{2}\left(\frac{\pi }{4}-x\right)$ and $g(x)=\sqrt{3}\sin\left(\frac{\pi }{4}+x\right)\cos\left(\frac{\pi }{4}+x\right)$ at points $P$ and $Q$, respectively, find the maximum length of the line segment $PQ$.

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