
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
In the rhombus \(ABCD\), point \(Q\) divides side \(BC\) in the ratio \(1:3\) starting from vertex \(B\), and point \(E\) is the midpoint of side \(AB\). It is known that the median \(CF\) of triangle \(CEQ\) is equal to \(2\sqrt{2}\), and \(EQ = \sqrt{2}\). Find the radius of the circle inscribed in rhombus \(ABCD\).

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