
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
Let  $ABC$  be an equilateral triangle . Let  point  $D$  lie on side  $AB,E$   lie on side  $AC, D_1$  and  $E_1$  lie on side BC such that  $AB=DB+BD_1$  and  $AC=CE+CE_1$ . Calculate the smallest angle between the lines  $DE_1$  and  $ED_1$ .

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