
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 $|a|=2$, $|b|=3$, the angle between $a$ and $b$ is $60^{\circ}$, $c=5a+3b$, and $d=3a+kb$, find the value of the real number $k$ such that

(1) $c$ is parallel to $d$;

(2) $c$ is perpendicular to $d$.

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