
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 $|\overrightarrow{a}|=4, |\overrightarrow{b}|=3, (2\overrightarrow{a}-3\overrightarrow{b})(2\overrightarrow{a}+ \overrightarrow{b})=61$.

1. Find $|\overrightarrow{a}+ \overrightarrow{b}|$;
2. If $\overrightarrow{AB}=\overrightarrow{a}, \overrightarrow{BC}=\overrightarrow{b}$, find the projection of vector $\overrightarrow{BA}$ on $\overrightarrow{BC}$;
3. Given that $\overrightarrow{a}- \overrightarrow{b}$ and $t\overrightarrow{a}+ \overrightarrow{b}$ form an obtuse angle, find the range of values for the real number $t$.

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