
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: $x^{10} = a + a_{1}(1-x) + a_{2}(1-x)^{2} + \ldots + a_{10}(1-x)^{10}$, where $a, a_{1}, a_{2}, \ldots, a_{10}$ are constants, calculate the value of $a + a_{2} + a_{4} + \ldots + a_{10}$.

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