
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
Bryan Ai has the following 8 numbers written from left to right on a sheet of paper:  $$ \textbf{1 4 1 2 0 7 0 8} $$  Now in each of the 7 gaps between adjacent numbers, Bryan Ai wants to place one of ` $+$ ', ` $-$ ', or ` $\times$ ' inside that gap.
Now, Bryan Ai wonders, if he picks a random placement out of the  $3^7$  possible placements, what's the expected value of the expression (order of operations apply)?

*Individual #10*

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