
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
Through the midpoint $D$ of the base of an isosceles triangle, a line is drawn at an angle of $30^{\circ}$ to this base, on which the angle $\angle ACB$ intercepts a segment $EF$. It is known that $ED = 6$ and $FD = 4$. Find the height of the triangle drawn to the base.

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