
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 $f(1,1)=1$, $f(m,n) \in \mathbb{N}^*$ for all $m,n \in \mathbb{N}^*$, and for any $m,n \in \mathbb{N}^*$, it holds that:
1. $f(m,n+1) = f(m,n) + 2$;
2. $f(m+1,1) = 2f(m,1)$. Find the value of $f(2007,2008)$.

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