
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 triangle \( \triangle ABC \), \( D \) is the midpoint of side \( BC \). As point \( E \) moves along line segment \( AD \), if \( \overrightarrow{BE} = \lambda \overrightarrow{BA} + \mu \overrightarrow{BC} \), then the minimum value of \( s = \lambda^2 + \mu \) is ____.

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