
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
In a general triangle $ABC$, mark the following points according to the diagram. Points $A_1$ and $B_1$ are the midpoints of sides $BC$ and $AC$, respectively. Points $C_1$, $C_2$, and $C_3$ divide side $AB$ into four equal parts. Connect points $A_1$ and $B_1$ with points $C_1$ and $C_3$ in a way that forms a bow enclosed by these connections. What fraction of the total area of the triangle does the bow occupy?

(M. Mach)

![Diagram](https://cdn.mathpix.com/cropped/2024_04_17_a28d21919b1f57221c31g-3.jpg?height=543&width=574&top_left_y=485&top_left_x=747)

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