
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 $ABC$, $AB=3$, $AC=4$, and $BC=5$. Point $O$ is the incenter, and vector $\overrightarrow{AO}$ can be represented as $\lambda_1 \overrightarrow{AB} + \lambda_2 \overrightarrow{BC}$. Find the value of $\lambda_1 + \lambda_2$.

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