
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
Let  $x_1$ ,  $x_2$ , …,  $x_{10}$  be 10 numbers.  Suppose that  $x_i + 2 x_{i + 1} = 1$  for each  $i$  from 1 through 9.  What is the value of  $x_1 + 512 x_{10}$ ?

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