
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
Given a triangle \( \triangle ABC \) with \( AB = 2 \), \( AC = 1 \), \( BC = \sqrt{7} \), and \( O \) as the circumcenter of \( \triangle ABC \). If \( \overrightarrow{AO} = \lambda \overrightarrow{AB} + \mu \overrightarrow{AC} \), find the value of \( \lambda + \mu \).

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