
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 a convex quadrilateral \(ABCD\), points \(E, F, H, G\) are the midpoints of segments \(AB, BC\), \(CD, AD\) respectively. \(O\) is the intersection point of segments \(EH\) and \(FG\). Given that \(EH = a\), \(FG = b\), and \(\angle FOH = 60^{\circ}\), find the diagonals of quadrilateral \(ABCD\).

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