
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 that the line $x=a\left(0<a<\frac{\pi}{2}\right)$ intersects the graphs of the functions $f\left(x\right)=\sin x$ and $g\left(x\right)=\cos x$ at points $P$ and $Q$ respectively, if $|PQ|=\frac{1}{4}$, then the ordinate of the midpoint of the line segment $PQ$ is ____.

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