
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 vectors $\overrightarrow{a}=(-1,2), \overrightarrow{b}=(3,4)$.

(I) If $(2\overrightarrow{a}-\overrightarrow{b}) \parallel (\overrightarrow{a}+k\overrightarrow{b})$, find the value of the real number $k$;

(II) If the projection of the vector $\lambda\overrightarrow{a}$ onto the direction of $\overrightarrow{b}$ is $1$, find the value of the real number $\lambda$.

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