
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 vectors \\( \overset{→}{e_1} =(1,0)\\), \\( \overset{→}{e_2} =(0,1)\\), \\( \overset{→}{a} = \overset{→}{e_1} -2 \overset{→}{e_2} \\), and \\( \overset{→}{b} =k \overset{→}{e_1} + \overset{→}{e_2} \\), find the value of the real number k if \\( \overset{→}{a} \parallel \overset{→}{b} \\).

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