
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 two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ forming an angle of 60°, with $|\overrightarrow{a}|=3$ and $|\overrightarrow{b}|=2$. If $\overrightarrow{c}=3\overrightarrow{a}+5\overrightarrow{b}$ and $\overrightarrow{d}=m\overrightarrow{a}-\overrightarrow{b}$:
(1) Find the value of $\overrightarrow{a} \cdot \overrightarrow{b}$;
(2) If $\overrightarrow{c} \perp \overrightarrow{d}$, find the value of the real number $m$.

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