
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
On the sides  $ AB $  and  $ AC $  of the triangle  $ ABC $  consider the points  $ D, $  respectively,  $ E, $  such that  $$  \overrightarrow{DA} +\overrightarrow{DB} +\overrightarrow{EA} +\overrightarrow{EC} =\overrightarrow{O} .  $$   
If  $ T $  is the intersection of  $ DC $  and  $ BE, $  determine the real number  $ \alpha $  so that:  $$  \overrightarrow{TB} +\overrightarrow{TC} =\alpha\cdot\overrightarrow{TA} .  $$  

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