
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 that point $O$ is a point in the plane of $\triangle ABC$, $4\overrightarrow{OA}•\overrightarrow{AC}={\overrightarrow{OC}^2}-1$, $4\overrightarrow{OC}•({\overrightarrow{OB}+\overrightarrow{OC}})=1-{\overrightarrow{OB}^2}$, then the maximum value of the angle between the vectors $4\overrightarrow{OA}+\overrightarrow{OB}$ and $2\overrightarrow{OA}-\overrightarrow{OC}$ is ____.

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