
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 measures, in degrees, of the angles ,  $\alpha, \beta$  and  $\theta$  are greater than  $0$  less than  $60$ . Find the value of  $\theta$  knowing, also, that  $\alpha + \beta = 2\theta$  and that   $$ \sin \alpha \sin \beta \sin \theta = \sin(60 - \alpha ) \sin(60 - \beta) \sin(60 - \theta ). $$  

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