
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 the angle between two forces $\overrightarrow{{F_1}}$ and $\overrightarrow{{F_2}}$ is $\frac{\pi}{2}$, the magnitude of their resultant force is $10N$, and the angle between the resultant force and $\overrightarrow{{F_1}}$ is $\frac{\pi}{4}$. Calculate the magnitude of $\overrightarrow{{F_1}}$.

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