
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
Outside the right-angled triangle $ABC$, squares $ACDE$ and $BCFG$ are constructed on its legs $AC$ and $BC$. The extension of the median $CM$ of the triangle $ABC$ intersects the line $DF$ at point $N$. Find the segment $CN$ if $AC = 4$ and $BC = 1$.

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