
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 $D$ and $E$ be points on sides $AB$ and $BC$ of $\triangle ABC$, respectively, with $AD = \frac{1}{2}AB$ and $BE = \frac{2}{3}BC$. If $\overrightarrow{DE} = \lambda_1 \overrightarrow{AB} + \lambda_2 \overrightarrow{AC}$ ($\lambda_1, \lambda_2$ are real numbers), then find the value of $\lambda_1 + \lambda_2$.

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