
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 three vectors in the plane: \\( \overrightarrow{a}=(1,-1)\\), \\( \overrightarrow{b}=(x,2)\\), and \\( \overrightarrow{c}=(2,1)\\), such that \\( \overrightarrow{a}\\) is parallel to \\( \overrightarrow{b}+ \overrightarrow{c}\\).
(I) Find the value of the real number \\(x\\);
(II) Find the projection of \\( \overrightarrow{c}\\) onto \\( \overrightarrow{a}- \overrightarrow{b}\\).

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