
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 the plane vectors $\overrightarrow {a}, \overrightarrow {b}$ that satisfy: $| \overrightarrow {a}|=4, | \overrightarrow {b}|=3, (2 \overrightarrow {a}-3 \overrightarrow {b})\cdot (2 \overrightarrow {a}+ \overrightarrow {b})=61$.

1. Find the angle θ between $\overrightarrow {a}$ and $\overrightarrow {b}$.
2. Find the projection of vector $\overrightarrow {a}$ on vector $3 \overrightarrow {a}+2 \overrightarrow {b}$.

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