
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 line $x=a (0 < a < \frac{\pi}{2})$ intersects with the graph of the function $f(x)=\sin x$ and the graph of the function $g(x)=\cos x$ at points $M$ and $N$, respectively. If $MN = \frac{1}{5}$, find the y-coordinate of the midpoint of the segment $MN$.

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