
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 the acute-angled triangle \( ABC \) intersect at point \( H \). Points \( M \) and \( N \) are the midpoints of segments \( AH \) and \( CH \), respectively. It is known that \( FM = 1 \), \( EN = 4 \), and \( FM \parallel EN \). Find the measure of \( \angle ABC \), the area of triangle \( ABC \), and the radius of the circumscribed circle around it. 

Answer: \( \angle ABC = 60^\circ \), \( S_{\triangle ABC} = 18 \sqrt{3} \), \( R = 2 \sqrt{7} \).

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