
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
The six sides of a convex hexagon  $A_1 A_2 A_3 A_4 A_5 A_6$  are colored red. Each of the diagonals of the hexagon is colored either red or blue. If  $N$  is the number of colorings such that every triangle  $A_i A_j A_k$ , where  $1 \leq i<j<k \leq 6$ , has at least one red side, find the sum of the squares of the digits of  $N$ .

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