
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
The altitudes $CF$ and $AE$ of an acute triangle $ABC$ intersect at point $H$. Points $M$ and $N$ are the midpoints of segments $AH$ and $CH$, respectively. It is known that $FM = 1$, $EN = 7$, and $FM \parallel EN$. Find the value of $\angle ABC$, the area of triangle $ABC$, and the radius of its circumscribed circle. 

Answer: $\angle ABC = 60^\circ$, $S_{\triangle ABC} = 45\sqrt{3}$, $R = 2\sqrt{19}$.

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