
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 $\overset{→}{a}$ and $\overset{→}{b}$ are unit vectors, and $|\overset{→}{a} + \overset{→}{b}| = \sqrt{2}|\overset{→}{a} - \overset{→}{b}|$, find the projection of $\overset{→}{a}$ on $\overset{→}{a} + \overset{→}{b}$.

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