
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 an isosceles triangle, we drew one of the angle bisectors. At least one of the resulting two smaller ones  triangles is similar to the original. What can be the leg of the original triangle if the length of its base is  $1$  unit?

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