
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 $\triangle ABC$, point $D$ satisfies $\overrightarrow{BD} = \frac{2}{3} \overrightarrow{BC}$. Point $E$ is a moving point on segment $AD$ (excluding endpoints). If $\overrightarrow{BE} = \lambda \overrightarrow{AB} + \mu \overrightarrow{AC}$, then $\frac{\lambda + 1}{\mu} =$ \_\_\_\_\_\_.

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