
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 function $f(x)=\cos (2x+ \frac {\pi}{4})$, if we shrink the x-coordinates of all points on the graph of $y=f(x)$ to half of their original values while keeping the y-coordinates unchanged; and then shift the resulting graph to the right by $|\varphi|$ units, and the resulting graph is symmetric about the origin, find the value of $\varphi$.

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